Allright, So you are given cot^-1(1)
The cot^(-1) means to find the angle where cot is 1
Cot is also (cos/sin)
So if you look at the unit circle, where does cos equal 1?
So cos is 2pi at 1
and sine is pi/2 at 1
If you put 2pi/pi/2 you get pi/4
So cos^-1(1) is pi/4